Problem 22 · 2017 Math Kangaroo
Stretch
Counting & Probability
Number Theory
careful-counting
The numbers −3, −2, −1, 0, 1, 2 are written on the six faces of a die. The die is rolled twice. The numbers that were rolled are multiplied. How big is the probability that this product is negative?
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Answer: E — 13
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Hint 1 of 2
A product is negative only when one factor is positive and the other is negative.
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Hint 2 of 2
Count the positive faces and the negative faces; zero never helps.
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Approach: count favourable ordered rolls over all 36 outcomes
- The faces are −3, −2, −1, 0, 1, 2: three negatives and two positives (0 gives product 0).
- Negative product needs one of each sign; ordered, that is 3·2 + 2·3 = 12 of the 36 equally likely pairs.
- Probability = 12/36 = 1/3, choice E.
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